# PH meter design

Hello!

I have a question concerning the functioning of a pH meter. All the sources online that I can find either omit, I think, important information, or describe it in "technical terms" with equations. I would like to know what is happening at the level of the distribution and movement of charge; after all, a pH meter, from my understanding, is simply measuring an electric potential difference.

Okay, so there is the reference electrode of a certain metal or compound and the corresponding solution. Generally, I believe this is AgCl electrode in a chloride solution (such as AgCl or HCl). An equilibrium is formed between the solid AgCl and the aqueous Cl- and Ag+ (and AgCl2-?), generating an electrode potential. If another electrode of the same type and with the same solution with the same concentration (i.e. two identical half-cells) are connected. There is zero electric potential difference between the two electrodes.
A second electrode of the same type is connected to the first, the reference electrode, via a voltmeter; this second electrode is called the glass electrode. The electic potential difference would therefore be zero between the two electrodes, as the electrodes and the solutions they are bathed in are identical.
I hope this is accurate so far. The next step takes into account the nature of the glass electrode half-cell. The glass electrode has a special glass membrane sorrounding the electrolyte solution that can sequester H+ ions on both sides of the membrane. When the glass membrane is therefore submerged in a solution of a pH different to the internal solution bathing the glass electrode, a potential difference is established across the glass membrane. This apparently, can be used to determine the pH of the solution, since the pH inside the membrane (bathing the electrode) is known, and there is a relationship between the H+ concentration inside, H+ concentration outside and the potential difference. So if the inside pH is known, the potential difference across the membrane is known, then the outside pH can be determined.
This I can understand; however, some of the sources I have read seem to claim that this is all that is needed, and everything else is constant, but if this was the case, how is a potential difference generated between the glass electrode and the reference electrode? If the two electrodes initially have a potential difference of zero, and it changes (or indeed ANY change is recorded on the voltmeter) then SOMETHING has to be changing between the two electrodes, which means both electrodes are changing in some way. If the voltmeter is accepted as having infinite resistance, then something is at least "attempting" to happen: in the case of a voltmeter connected to a battery, the electrons would be attempting to flow from the negative electrode to the positive electrode, which is where the reading comes from. In the case of the pH meter, if the voltmeter, positioned between the two electrodes, changes, then electrons are at least attempting to move ("attempting" if infinite resistance is accepted for the voltmeter). If electrons are attempting to move between the electrodes, then the electrodes are attempting to change in some fashion, and the electric potential across the glass membrane is affecting the electrodes.
I was wondering, therefore, if it has to do with the response on the inside of the glass membrane; say, for example, that the pH was higher outside. This would draw H+ ions inside close to the surface, as they are attracted to the relatively negative charge outside. This sequestration of H+ ions inside (they are "taken out" of solution and held close to the surface of the glass membrane) alters the internal pH local to the glass electrode; this then alters the equilibrium between the ions in solution and the depositon of the atoms on to the electrode, altering the electrode potential. This would then create a difference in electrical potential between the two electrodes: the reference electrode and the glass electrode. Fundamentally, I imagine it as the glass membrane is used to store of release H+ ions into the glass electrode's bathing solution, altering the pH and therefore altering the electrode potential (which is pH-dependent).
I suspect this is wrong, but I can't see otherwise how a difference in potential is created between the reference electrode and the glass electrode without the glass electrode's potential being altered in some way. There can't simply be a difference across the glass membrane that is measured, otherwise what it the point of the glass electrode and the reference electrode.

Any help is much appreciated.
I found this quite difficult to describe, I can upload some pictures drawn with my excellent artistry if that would help.

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Borek
Mentor
Sorry, I did my best to follow and to understand where the problem is, but to no avail.

Hi Borek,

Apologies if the post was long, but I believe there is a lot happening in a pH meter.

Basically, I want to know how a pH meter works. I can't find an online source that goes step by step, without making assumptions about the readers knowledge or omitting important information.

I will try again, trying to keep it brief!
Assuming a voltmeter has infinite resistance, no charge is moving, but to have a non zero voltage means charge "wants" or is "attempting" to move. As such, something can be said to be happening in the circuit, or at least attempting to happen. I gave an example of a battery connected to a resistor. With this in mind, if the reading on a pH meter can be changed, then something must be happening, or attempting to happen, at the electrodes; as such, the electrodes can't be said to be doing nothing.

There are two electrodes in a pH meter. Both are bathed in an electrolyte solution, and the electrodes are connected by a voltmeter. Ions will leave the electrode and enter the electrolyte solution and vice versa, and an equilibrium will be established; this will produce a charge on the electrode; I believe this is called the electrode potential. The relative difference in charges between the electrodes will produce a voltage. Assuming the electrodes and electrolytes are identical - it doesn't matter if they are or not, I don't think, but for simplicity I'll make that assumption - then the voltage is zero.

The reference electrode doesn't directly interact with a test solution other than via a salt bridge. The glass electrode has a glass bulb surrounding the electrolyte solution; the electrode itself isn't glass, it's called a glass electrode because of the glass bulb. This glass bulb is placed in a test solution and the hydrogen ions in that solution "interact" with the glass bulb. The hydrogen ion concentration inside the glass bulb doesn't change. The pH of a test solution doesn't have to be a specific value, and so different test solutions can have different values. So let's say the glass electrode and the reference electrode are placed into a solution with a different hydrogen ion concentration than the electrolyte solution inside the glass bulb, bathing the glass electrode (and the reference electrode, which for our purposes has the same make-up as the solution bathing the glass electrode). What happens next?

From what I have read, a voltage is generated across the glass bulb, since there is a difference in charge on either side of the glass bulb. Some sources claim the pH inside the glass bulb remains fixed, but it can't be as simple as saying that, since it implies nothing is happening to the electrode, I can't find a single source that describes what's happening to the electrode. Here's where I don't understand what is happening. If a voltage is produced between the electrodes, SOMETHING has to be happening, or attempting to happen, and the relationship between the electrodes has changed; charge is attempting to flow. If the reference electrode doesn't DIRECTLY interact with the test solution, then something is affecting the glass electrode. The voltage generated across the glass is affecting the glass electrode. If my reasoning is in any way accurate, then my question is: how does the voltage across the glass bulb affect the glass electrode? That's the crux of my issue.

I can understand that the OVERALL hydrogen ion concentration is fixed inside the glass bulb, as they have nowhere to go. However, I can imagine the surface of the glass bulb "holding" the hydrogen ions, or releasing them, and altering the hydrogen ion concentration local to the glass electrode itself. Since pH affects the equilibrium between ions entering solution and joining the electrode, the electrode potential for the glass electrode has changed (or attempts to change, assuming infinite resistivity of the voltmeter), and the voltage between the glass electrode and the reference electrode changes, producing a voltage (or atleast, attempts to change). I think pH actually has more to do with hydrogen ion activity than concentration, but I guess that's not important here. The important point is that the pH local to the glass electrode has changed, as has the pH local to the surface of the glass bulb on the inside, but overall the pH hasn't changed; this reconciles my position with the sources I have read, but fundamentally, something has to be happening, or attempting to happen, at the electrodes, otherwise there is no voltage between them, it remains constant at zero.

I hope this is a little clearer. My main question is in bold, assuming the rest of what I said previous to the question is reasonable.

Thank you in advance for any help.

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Borek
Mentor
Actually I don't think I have ever read a better explanation to the glass electrode working than handwavy "glass is so thin, protons can travel through it, so the circuit is closed".

If that's not the case (or, to put it slightly differently - if the charge doesn't flow through the glass) I have no idea how the pH meter works. This is a rather basic physics of the circuits, voltmeter requires some charge transfer to operate, you can't change it just because pH is a chemical concept.

Thanks for the response Borek. I found some useful sources which I will try to add when I can access a computer. Doing it on a tablet is difficult.

Just briefly, let's say hydrogen ions, or as some sources suggest, sodium ions cross the glass bulb (if, incidentally, hydrogen ions do cross the glass bulb, then the electrolyte solution bathing the glass electrode doesn't have a constant pH). If the ions do cross, what effect does this have on the AgCl electrode? Something must happen, or "attempt" to happen, to the electrode. Otherwise, there is no change in voltage between the two electrodes: the voltmeter is placed between the glass electrode and the reference electrode.

Additionally, if you alter part of a circuit, it affects the entire circuit. We can look at the changes and say which bit has been manipulated to produce the change, but to get a different voltage in the circuit means the flow of charge through the entire circuit is altered. Is that in anyway accurate?

Borek
Mentor
Currents present are so low changes in the composition are completely negligible.

Just to get some rough numbers. We deal with 59 mV per pH unit. That gives us voltage in the tenths of volt range. Make it 1 V to make things easier. Let's say we use a lousy 10 MΩ internal resistance voltmeter (good ones are in the GΩ range). That means current in the 0.1 μA range. Assuming 1 electron reaction we have $\frac {0.1 \mu A \times 1 s}{96500 \frac C {mol}} = 1\times 10^{-12} mol$ reacting per second - and typical cell contains substances in the mmol or μmol range, million times more in the worst case scenario.

The very tip of the glass (not the external reference) electrode is the permeable part, a thin glass membrane, in the past often a Corning 015 glass. The rest of the electrode is actually an internal reference electrode not responsive to pH. Today the tips are better made with different compositions to give more accurate values at extreme pH. The protons replace cations on the membrane surface resulting in a thin acid gel. The meter, as all potentiometic meters, measures activity rather than concentration. This doesn't really address your question, but I thought you might find it interesting and point you to other literature.

Currents present are so low changes in the composition are completely negligible.

Thanks for the reply Borek. I assumed this might be the case. This relates to the point I made earlier regarding the theoretical "infinite resistance" of a voltmeter: in that case, there wouldn't be any change, but an "attempt" to change is present. In reality, something is changing at the electrodes, and I am interested to know what it is. It must surely connect to the equilibrium between ions joining and leaving the electrode. That seems to me the only way that the voltage between the electrodes can change, with a change in relative charge on the two electrodes.

The very tip of the glass (not the external reference) electrode is the permeable part, a thin glass membrane, in the past often a Corning 015 glass. The rest of the electrode is actually an internal reference electrode not responsive to pH. Today the tips are better made with different compositions to give more accurate values at extreme pH. The protons replace cations on the membrane surface resulting in a thin acid gel. The meter, as all potentiometic meters, measures activity rather than concentration. This doesn't really address your question, but I thought you might find it interesting and point you to other literature.

Hi AgentSmith, thanks for the response. Can activity not be approximated with concentration? I was under the impression activity is essentially, to do with the number of a species available "to do stuff". Regarding the replacement of cations. I read that it may be Na+ ions that enter into the electrolyte solution bathing the electrode. I was wondering if maybe the Na+ ions would have an effect on the electrode potential. It just seems to me something has to be happening to the electrodes (or, at least, one of them: the glass electrode).

Borek
Mentor
Can activity not be approximated with concentration?

Approximated - yes. For infinitely diluted solutions activity equals concentration. The more concentrated the solution, the higher the discrepancy between concentration and observed activity.

Actually it is ionic strength of the solution that is typically most important, see a very short intro here: http://www.chembuddy.com/?left=pH-calculation&right=ionic-strength-activity-coefficients